Reconstruction accuracy of the surface detector array of the Pierre Auger Observatory

Abstract

The reconstruction of extensive air showers (arrival direction, core position and energy estimation) by the surface detector of the Pierre Auger Observatory is discussed together with the corresponding accuracy. We determine the angular reconstruction accuracy as a function of the station multiplicity by using two different aproaches. We discuss statistical and systematic uncertainties in the determination of the signal at 1000 m from the core, S(1000), which is used to estimate the primary energy.

Full text

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arXiv:0709.2125v1 [astro-ph] 13 Sep 2007
30th International Cosmic Ray Conference
Reconstruction accuracy of the surface detector array of the Pierre Auger
Observatory
M. Ave for Pierre Auger Collaboration1
1Pierre Auger Observatory, Av San Mart´ ın Norte 304,(5613) Malarg¨ ue, Argentina
ave@cfcp.uchicago.edu
Abstract: The reconstruction of extensive air showers (arrival direction, core position and
energy estimation) by the surface detector of the Pierre Auger Observatory is discussed to-
gether with the corresponding accuracy. We determine the angular reconstruction accuracy
as a function of the station multiplicity by using two different aproaches. We discuss statisti-
cal and systematic uncertainties in the determination of the signal at 1000 m from the core,
S(1000), which is used to estimate the primary energy.
Introduction
The Pierre Auger Observatory consists of two
independent components: the fluorescence de-
tector (FD) and the surface detector (SD)
[1]. We have determined the angular reso-
lution of events recorded by the surface de-
tector alone, on an event by event basis,
from the zenith (θ) and azimuth (φ) uncer-
tainties obtained from the geometrical recon-
struction, using the relation described in [2]:
F(η) = 1/2 (V [θ] + sin2(θ) V [φ]) , where η
is the space-angle, and V [θ] and V [φ] are the
variance of θ and φ respectively. We define
the angular resolution (AR) as the angular ra-
dius that would contain 68% of showers com-
ing from a point source, AR = 1.5
We checked the angular resolution using the re-
dundant information given by a sub-array com-
posed by adjacent detectors.
The parameter used to infer the energy of the
surface detector events (S(1000)) is studied
and its systematic and statistical errors are de-
termined. The event-by-event error estimation
is checked with full Monte Carlo simulations .
The unavoidable fluctuations in this parameter
caused by fluctuations in the shower develop-
ment is evaluated with simulations for different
primary assumptions.
?F(η).
Angular Resolution
The arrival direction of a SD event is deter-
mined by fitting the arrival time of the first
particle in each station to a showerfront model.
The precision achieved in the arrival direction
depends, on the clock precision of the detector
and on the fluctuations in the first particle ar-
rival time. In [3] an empirical model has been
developed to determine the uncertainty in the
time measurement of each individual detector
participating in the event.
The model of the shower front used in the min-
imization procedure, be it spherical, parabolic,
or even planar also influences the uncertainty
in the arrival direction determination, but not
as much as the time measurement precision. It
has been shown in [3] that a parabolic model
for the shower front adequately describes the
data.
On a event by event basis
Given the two inputs: a model for the time
variance and a model for the shower front,
the angular resolution can be calculated on
an event by event basis out of a minimiza-
tion procedure.In Fig. 1, we show our an-
gular resolution as a function of the zenith an-
gle for various station multiplicities (circles: 3
stations, squares: 4 stations, up triangles: 5

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Short title
0
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
010203040 5060
θ (degrees)
Angular Resolution (degrees)
3 stations
4 stations
5 stations
6 or more stations
Figure 1: Angular resolution (AR) for the SD
as a function of the zenith angle (θ). The AR
is plotted for various station multiplicities.
stations, down triangles: 6 stations or more).
The data used to build this plot spans from
January/2004 to March/2007.
As it can be seen, the angular resolution is bet-
ter than 2◦in the worst case of vertical showers
with only 3 stations hit. This value improves
significantly for 4 or 5 stations1. For 6 or more
stations, which corresponds to events with en-
ergies above 10 EeV, the angular resolution is
in all cases better than about 1◦.
Using station pairs
A new sub-array of pairs has been recently de-
ployed as a part of the Surface Detector array.
These are adjacent detectors located ∼ 11 m
apart, and therefore are sampling the same re-
gion of the shower front. To do this analysis,
events with at least three pairs are selected.
The reconstruction is then performed twice,
each time using the time information of one
of the tanks in each pair. This provide two
quasi-independent estimates of the geometry.
In Fig. 2 we show the space-angle difference
between these two estimates for showers with
3, 4, and 5 or more stations.
The distributions are then fitted to the ad-
justed Gaussian resolution function (dp ∝
e−η2/2σ2
d(cos(η)) dη, where η is the angle
between the two reconstructions of the same
shower) to obtain σ. The angular resolution
(68% contour), which is given by 1.5 times σ, is
0
50
100
150
012345
3 stations
4 stations
Entries
Mean
RMS
χ2 / ndf
σ
995
1.33
0.78
39.62 / 14
1.06 ± 0.02
0
10
20
30
012345
5 stations or more
Entries
Mean
RMS
χ2 / ndf
σ
163
1.13
0.77
20.06 / 13
0.79 ± 0.05
0
5
10
15
20
012345
Entries
Mean
RMS
χ2 / ndf
σ
72
0.88
0.61
15.96 / 8
0.60 ± 0.04
Space-angle difference (degrees)
Figure 2: Space-angle difference between two
SD estimates of the event geometry for differ-
ent multiplicities (see text for more details).
in agreement with the one obtained on a event
by event basis.
Energy Estimator
The surface detector only samples the proper-
ties of an air shower at a limited number of
points at different distances from the shower
axis (r). An observable has to be then defined
to estimate the shower size. To avoid the large
fluctuations in the signal integrated over all
distances caused by fluctuations in the shower
development, Hillas [4] proposed to use the sig-
nal at a given distance (S(r)) to classify the
size of the shower. In Fig. 3 we show the pre-
dictions from Monte Carlo simulations of the
magnitude of the fluctuations in S(r = 1000)
as a function of zenith angle. The relative fluc-
tuations are found to be independent of energy
and its magnitude is ∼ 10% for most of the
cases studied.
The experimental error in the estimation of the
signal size at a given core distance depends on
the spacing of the array. In [5] it has been
shown that for the Auger array spacing the
1. For 4 and 5 stations the AR is very similar
because in the fitting procedure they have the same
number of degrees of freedom.

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30th International Cosmic Ray Conference
sec theta
1 1.11.21.31.41.51.61.7 1.81.92
1000
) / S
1000
RMS(S
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Figure 3: Relative spread due to shower to
shower fluctuations for different compositions
(blue-iron, red-proton, black-mixed composi-
tion).
optimum distance (ropt) to minimize this ex-
perimental error is ∼1000 m. Therefore, the
observable that we use to relate to the pri-
mary energy will be the signal size at 1000 m
(S(1000))2. However, it should be noted that
ropt fluctuates from event to event and in-
creases to larger core distances (∼ 1500 m)
when there are saturated stations [5].
To estimate S(1000) it is necessary to adopt
a lateral distribution function (LDF) that de-
scribes the fall-off of the signal size with the
distance to the shower axis. The function used
here is a modified NKG function given by:
S(r) = S(1000)?
the distance to the shower axis in meters, S(r)
is the signal size at a core distance r, S(1000)
is the size parameter of the shower, and β is
called the slope of the LDF.
r
1000
?−β?r+700
1700
?−β, where r is
S(1000) uncertainties
The signal sizes in each station are then used
to estimate the core location and S(1000), with
β being a fixed parameter. The fitting error
in S(1000) is a consequence of the uncertainty
of the observed signal size largely due to the
finite dimension of the detectors. This will be
the statistical error in S(1000) (σstat
uncertainty in the signal sizes has been mea-
sured directly using pairs of stations located
close to each other in the field [6].
The second source of error in S(1000) is a
systematic (σsys
S(1000)) arising from the lack of
knowledge of the true LDF shape for a par-
S(1000)). The
Figure 4:
tistical error in S(1000) as a function of
log S(1000). The data has been divided in two
sets (events with-without stations saturated).
The average systematic and sta-
ticular event. If the ropt of a given event is
close to 1000 m, the fitted S(1000) is indepen-
dent of the value of β assumed [5]. When it is
not, fluctuations in the event by event β give
rise to a systematic error. The value of β to
be used in the reconstruction has been esti-
mated empirically: in a small subset of events
(S(1000) > 20 VEM and having more than 5
stations) the β is left as a free parameter as
well. We then parameterize the fitted values of
β as a function of zenith angle and S(1000).
The deviation from this parameterization is
calculated for each event and the RMS (σβ)
parameterized as a function of S(1000) (no
dependence on zenith angle has been found).
The result is the following: σβ(S(1000)) =
0.71×exp(−0.976 log(S(1000))). We then re-
peat N times the reconstruction of each event,
fixing β to values sampled from a Gaussian dis-
tribution centered around the prediction with
the sigma given above. The RMS of the fit-
ted S(1000) from these set of fits is then the
systematic error of S(1000) (σsys
S(1000)).
In Fig. 4 we show the average systematic and
statistical error of S(1000) as a function of
log(S(1000)). The data has been divided in
two sets: events with (without) saturated sta-
2. S(1000) is measured in units of VEM, i.e. the
signal produced by a vertical centered muon.

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Short title
Figure 5: Total error in S(1000) calculated on
an event by event basis from the data. The
data is separated in two sets:
(without) saturated stations.
respond to the predictions from full MC calcu-
lations (see text for details)
events with
The lines cor-
tions. Two features are clearly seen: a) the
error in events with saturated stations is sys-
tematically 5% larger, b) σstat
the error budget for S(1000) <40 VEM. No de-
pendence of σsys
has been found.
S(1000)dominates
S(1000)or σstat
S(1000)on zenith angle
Using Full Monte Carlo Simulations
To benchmark our error estimation we have
created a library of Corsika showers for pro-
ton primaries, zenith angles θ= 0-12-25-36-
45-60 degrees and energies log10E(eV )=17.8-
18.0-18.2-18.4-18.6-19.0-19.5-20.0.
Corsika shower, we calculate the true S(1000)
and it is then used to generate 10 (25) events
(depending on the energy) with random core
positions.
The reconstruction procedure used for the data
is then applied to the simulations. For each
zenith angle and energy we fit the distribu-
tion of log
?
S(1000)true
tion. The mean value and sigma are then pa-
rameterized as a function of S(1000)true. No
zenith angle dependence has been found. A
bias in the reconstructed S(1000) is only found
for S(1000) < 10 VEM. The sigma of this dis-
tribution is the quadrature combination of the
For each
S(1000)rec
?
to a Gaussian func-
statistical and systematic error in S(1000). In
Fig. 5 we show the comparison of the sigma of
these distributions with the average total error
obtained on an event by event basis. The data
is separated in two sets: events with (without)
saturated stations. The circles correspond to
the total error obtained on a event by event
basis, the lines are the predictions from full
Monte Carlo simulations.
excellent except for a slight overestimation of
the error (∼4%) for saturated events at large
energies.
The agreement is
Conclusions
The angular resolution of the surface detec-
tor was determined experimentally, checked us-
ing the pairs data set and found to be bet-
ter than 2◦for 3-fold events (E < 4 EeV),
better than 1.2◦for 4-folds and 5-folds events
(3 < E < 10 EeV) and better than 0.9◦for
higher multiplicity events (E > 10 EeV).
The error of the parameter used to infer the en-
ergy of the surface detector events (S(1000))
has been determined experimentally, checked
using full Monte Carlo simulations and found
to be better than 8% (12%) at the highest en-
ergies for events with (without) saturated sta-
tions.At high energies, the fluctuations in
S(1000) are dominated by fluctuations in the
shower development.
References
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NIM 523 (2004) 50.
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[4] A.M.Hillas et
Academiae Scietiarum Hungaricae 29,
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[5] D. Newton et al., Astropart. Phys. 26
(2007) 414-419.
[6] M. Ave et al, NIM 578 (2007), 180-184
al., ActaPhysica